Mexico City lowered its swine flu alert level from yellow to green late last night as the mayor, Marcelo Ebrard, claimed residents could "relax" as there had been no new infections for a week.

Ebrard said the change meant the risk of contagion was low, the situation was under control and the images of countless people wearing blue surgical masks around the city could be consigned to history.

There's no longer any need to wear masks, Ebrard said, adding: "Now you can come to the city without any risk."

With fears of an immediate global pandemic fading, Japan, where there have been almost 300 swine flu cases, also relaxed rules amid fears that the strict regulations could harm the economy and put needless restrictions on the public.

"It is important to make it possible for the local government to respond flexibly, depending on the situation of the region," the prime minister, Taro Aso, said.

Under the new guidelines, suspected patients in areas where the number of cases are rapidly increasing would be allowed to go to regular medical clinics rather than only designated "fever centres" set up to deal with swine flu, the health minister, Yoichi Masuzoe, said.

In Italy, two secondary schools in Rome have been ordered to close for a week after four students caught the H1N1 flu virus on a trip to New York.

In Mexico, where 75 swine flu deaths have occurred, the health authorities said no one had been taken to hospital with respiratory infections in the past three days. There have been no confirmed swine flu cases since May 14.

"We are seeing a 96% drop in cases and that's why we are dropping the alert level to green today," the Mexico City health secretary, Armando Ahued, said.

Since the outbreak was declared on 23 April, Mexico City has spent 4.5bn pesos (£217m) on medicine and antibacterial gel and to provide incentives for businesses to shut their doors and to clean public spaces.

A total of 4,008 people have been infected in Mexico. The country's confirmed toll has been rising as scientists test a backlog of samples from patients.

Ebrard urged Mexicans to remain vigilant, to maintain sanitary conditions in places where crowds gather such as the metro system and schools, and to support a "culture of health".

"The big lesson is that we understand what the scientists have been saying for a decade: that we have to be prepared for any possible virus that can appear," the mayor said.

Nearly 80% of those who died were between 20 and 54, according to the health department. However, many suffered from underlying medical conditions. Almost 30% were obese or had other metabolical problems, and 13% had ­cardiovascular problems.

New test results from the US Centres of Disease Control show that people in their 60s and older have signs of greater immunity to the new swine flu virus.

Scientists think that is because older people have been exposed to other viruses that are more similar to swine flu than more recent seasonal flu.